Rochelle and Irene do some fundraising for their sporting team. Together they raised $741.
If Irene raised $p, and Rochelle raised $199 more than Irene:
Solve for the value of P

Answer:

1. \(a = 8\)

2. \(b = \frac{1}{8}\)

3. \(c = 2 \frac{3}{5}\)

4. \(d = \frac{13}{50}\)

Step-by-step explanation:

The rule of the pattern follows that each successive number is 3 lesser than the preceeding Value.

The first term = 65

Second term = 65 - 3 = 62

Third term = 62 - 3 = 59

Fourth term = 59 - 3 = 56

Fifth term = 56 - 3 = 53

Sixth term = 53 - 3 = 50

Therefore, each successive number is reduced by 3.

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The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.

The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.

The length of the rectangular field = 70 meters

The width of the rectangular field = 50 meters

The width of the path around the field = Uniform width

Area of the path around the field = 104 m²

Let x represent the width of the path, we get;

(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104

4·x² + 240·x = 104

4·x² + 240·x - 104 = 0

The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;

\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;

a = 4, b = 240, c = -104

Therefore;

\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)

x ≈ 0.430 or x ≈ -60.4

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Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

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The surface areas of the figures are 336, 82 and 836

From the question, we have the following parameters that can be used in our computation:

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

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The surface area of the prisms are

1. 336 cm²

2. 82 m²

3. 836 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as;

SA = 2B +pH

where B is the base area , p is the perimeter and h is the height.

1. SA = 2B +ph

B = 1/2 × 6 × 8

= 24 m²

p = 6+8+10 = 24m

h = 12m

SA = 2 × 24 + 24 × 12

= 48 + 288

= 336 cm²

2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)

= 2( 6+21+14)

= 2( 41)

= 82 m²

3. SA = 2πr( r +h)

= 2 × 3.14 × 7( 7 + 12)

= 44( 19)

= 836 cm²

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base x height or side x side.

Step-by-step explanation:

to find the area, you multiply a number x a number. the fomula is base x height or side x side.

The rate at which the depth is changing at 3 a.m. is given as follows:

1.9919 feet per hour.

The function for this problem is given as follows:

D(t) = 2cos(πt/3 + 2π/5) + 5.

Giving the depth of the waves in t hours after midnight.

3 a.m. is three hours after midnight, hence the rate of change is given as follows:

D'(3).

Applying the chain rule, the derivative is given as follows:

D'(t) = -2π/3sin(πt/3 + 2π/5)

Hence, when t = 3, the derivative is given as follows:

D'(3) = -2π/3sin(π + 2π/5)

D'(3) = 1.9919 feet per hour.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

\(y = -\frac{1}{3}x + 4\)

Step-by-step explanation:

Required

Equation of line

passes through \((6,2)\)

In an equation of the form \(y =mx + b\); the slope is \(m\)

So, by comparison;

The slope of \(y = 3x + 1\) is: \(m =3\)

From the question, we understand that the required equation is perpendicular to \(y = 3x + 1\)

This means that its slope is:

\(m_2 =-\frac{1}{m}\)

So, we have:

\(m_2 =-\frac{1}{3}\)

The line equation is:

\(y = m_2(x - x_1) + y_1\)

Where:

\((x_1,y_1) = (6,2)\)

So, we have:

\(y = -\frac{1}{3}(x - 6) + 2\)

\(y = -\frac{1}{3}x + 2 + 2\)

\(y = -\frac{1}{3}x + 4\)

A proportional relationship has a constant rate of change.

The given statement is true.

Step-by-step explanation:

A proportional relationship has a constant rate of change. We need to tell if this statement is true or false

A proportional relationship is given by equation:

where y is dependent variable while x is independent variable and k is constant of proportionality

The constant of proportionality is constant for all the values of y and x.

So, A proportional relationship has a constant rate of change.

The given statement is true.

The constant of proportionality (k) tells you how steep the graph of a proportional relationship is TRUE.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Let's consider a proportional relationship

y∝ x

y = kx

k = y/x

Now the value of y directly depends on upone k.

So, changing k will change the steepness of the line.

Hence "The constant of proportionality (k) tells you how steep the graph of a proportional relationship is TRUE".

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In accordance with the exponential model, the current forest area is equal to 2801.149 square kilometers after six years.  

According with statement, the forest area decreases exponentially in time. Then, the exponential model is defined by following model:

n(x) = n' · (1 - r)ˣ

Where:

If we know that n' = 4400 km², r = 0.0725 and x = 6 yr, then the current forest area is:

n(6) = 4400 · (1 - 0.0725)⁶

n(6) = 2801.149

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Answer:

1/2 feet per second.

Step-by-step explanation:

Answer: D

Step-by-step explanation:

This is a translation, so this means side lengths are preserved because a translation is a rigid motion. If all the side lengths are the same, then the perimeters must be the same.

Answer: 3r

Step-by-step explanation: because 2r+1r=3r

Answer:

the interest earned is $50.22.

the balance of the account is $975.22.

Step-by-step explanation:

a. To find the interest earned, we can use the formula:

Interest = Principal x Rate x Time

where the Principal is $925, the Rate is 2.3% expressed as a decimal (0.023), and the Time is 2.4 years.

Interest = $925 x 0.023 x 2.4

Interest = $50.22

Therefore, the interest earned is $50.22.

b. To find the balance of the account, we need to add the interest earned to the initial principal:

Balance = Principal + Interest

Balance = $925 + $50.22

Balance = $975.22

Therefore, the balance of the account is $975.22.

By evaluating the given linear relation, we conclude that the complete table is:

x:  2, 0, 1, 14/3

y: 0, -3, -3/2, 4

Here we have the linear relation:

9x - 6y = 18

And we want to complete the given table, to do so, we just need to evaluate the relation in the given values and with that we can find the missing ones.

For example, the first pair has y = 0.

Evaluating that we get:

9x - 6*0 = 18

9x = 18

x = 18/9 = 2

Then we have the pair (2, 0).

The second has x = 0, replacing that we get:

9*0 - 6*y = 18

y = 18/-6 = -3

So we have the pair (0, -3)

The third has x = 1, replacing that:

9*1 - 6y = 18

-6y = 18 - 9 = 9

y = 9/-6 = -3/2

So we have the pair (1, -3/2)

The last value on the table is y = 4, replacing that:

9x - 6*4 = 18

9x - 24 = 18

9x = 18 + 24 = 42

x = 42/9 = 14/3

Then the complete table is:

x:  2, 0, 1, 14/3

y: 0, -3, -3/2, 4

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The number of dominoes are in each row for the artist is 42 dominoes.

From the information, the domino artist has 6 sets of 28 Domino’s. The total Domino will be:

= Number of set × Amount in each set

= 6 × 28

= 168

Since she arranges all the dominoes into four equal rows. This will be:

= Total number / Rows

= 168 / 4

= 42

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You are requested to provide an estimate of the building's total window cleaning expense so that the board can make a decision.

Some window cleaners charge by the hour, though the majority bill by the square foot or the number of windows. For home work, professionals bill between $40 and $75 per hour.

Due of the increased safety dangers in high-rises, they usually charge $85 per hour. Many cleaners may charge by the pane if the house is medium-sized, anything from $2 to $7 for each one or more for larger windows. It's typical to charge an hourly rate in large homes when counting each window by itself would take too long or be impossible.

Window cleaning costs typically run between $40 and $75 per hour. If the house is medium-sized, many cleaners may charge per the pane; for larger windows, they may charge anywhere from $2 to $7 for each one or more.

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You are requested to provide an estimate of the building's total window cleaning expense so that the board can make a decision.

Some window cleaners charge by the hour, though the majority bill by the square foot or the number of windows. For home work, professionals bill between $40 and $75 per hour.

Due of the increased safety dangers in high-rises, they usually charge $85 per hour. Many cleaners may charge by the pane if the house is medium-sized, anything from $2 to $7 for each one or more for larger windows. It's typical to charge an hourly rate in large homes when counting each window by itself would take too long or be impossible.

Window cleaning costs typically run between $40 and $75 per hour. If the house is medium-sized, many cleaners may charge per the pane; for larger windows, they may charge anywhere from $2 to $7 for each one or more.

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The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Number of electricians= 4

Number of hours= 6

Now,

We can use the formula:

workers × time = work

where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.

In this case, we know that 4 electricians can complete the job in 6 hours. So:

4 × 6 = work

work = 24

This means that the total amount of work required to complete the job is 24 "units".

Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".

So we have:

3 × t = 24

Dividing both sides by 3, we get:

t = 8

Therefore, by work and time answer will be 3 electricians and 8 hours.

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Answer:

23-22=1

5 times 4=20

Step-by-step explanation:

Answer:

The figure is a triangular prism

Step-by-step explanation:

it's bc the bases are triangles

A triangular prism is a three-sided prism consisting of a triangular base, a translated duplicate, and three faces connecting similar sides. The given net will form a triangular prism.

A triangular prism is a three-sided prism consisting of a triangular base, a translated duplicate, and three faces connecting similar sides. A right triangular prism has rectangular sides and is oblique otherwise.

A triangular prism is a three-sided prism consisting of a triangular base, a translated duplicate, and three faces connecting similar sides. The given net will form a triangular prism.

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Answer:

46 boxes

Step-by-step explanation:

1012 / 22 = 46

Step-by-step explanation:

the slope of a line is the ratio y/x.

that means when going from one point to the other, how many units is y changing, when x changes a certain number of units.

so, going from one point to the other here, x changes by 30 units (from -12 to +18). and y changes 15 units (from -9 to 6).

therefore, the slope is

15/30 = 1/2

Answer:79

Step-by-step explanation:

Answer:

Step-by-step explanation:

15% of 20 is 3

Answer:

both

Step-by-step explanation:

get a line graph

Answer: 0.0622009569378

Step-by-step explanation: